on taking \(v_{+}=0\) , which is assuming that the resonant wavetrain sits on the initial level \(u_{+}\)  ahead.
If \(s_{+} \le 2u_{+}/\sqrt{q}\) , then there is no resonant wavetrain ahead of the DSW, which is the PDSW regime
illustrated in Figure REF (a). If \(s_{+} > 2u_{+}/\sqrt{q}\) , then the DSW sheds a resonant wavetrain ahead
of it as the group velocity \(c_{g} = k_{r}\)  of the resonant wavetrain is greater than its phase velocity,
\(c < c_{g}\)  [1]}, [2]}, on using (REF ) and (REF ).
Resonance can then
occur if \(s_{+} \ge 2u_{+}/\sqrt{q}\) . If this condition is not satisfied, then there is just a DSW and we have the PDSW regime.
